Question

what is m∠2 + m∠3? explain.
o a. 180; m∠1 + 90 = 180, so m∠2 + m∠3 = 180.
o b. 180; m∠1 + 90 = m∠2 + m∠3, so m∠2 + m∠3 = 180.
o c. 90; m∠1 + m∠2 + m∠3 = 180. m∠1 = 90, so m∠2 + m∠3 = 90.
o d. 90; ∠2 and ∠3 are corresponding angles, so m∠2 + m∠3 = 90.

Explanation:

Step1: Identify angle - sum property

The sum of angles in a triangle formed by the intersection of the lines is 180 degrees. Here, $\angle1+\angle2+\angle3 = 180^{\circ}$.

Step2: Determine the measure of $\angle1$

We can see that $\angle1 = 90^{\circ}$ (right - angle).

Step3: Calculate $\angle2+\angle3$

Substitute $\angle1 = 90^{\circ}$ into $\angle1+\angle2+\angle3 = 180^{\circ}$. We get $90^{\circ}+\angle2+\angle3 = 180^{\circ}$. Then $\angle2+\angle3=180^{\circ}-\ 90^{\circ}=90^{\circ}$.

Answer:

C. 90; $m\angle1 + m\angle2 + m\angle3 = 180$, $m\angle1 = 90$, so $m\angle2 + m\angle3 = 90$